Problem: Simplify the following expression: $\dfrac{9z^5}{54z^3}$ You can assume $z \neq 0$.
Explanation: $ \dfrac{9z^5}{54z^3} = \dfrac{9}{54} \cdot \dfrac{z^5}{z^3} $ To simplify $\frac{9}{54}$ , find the greatest common factor (GCD) of $9$ and $54$ $9 = 3 \cdot 3$ $54 = 2 \cdot 3 \cdot 3 \cdot 3$ $ \mbox{GCD}(9, 54) = 3 \cdot 3 = 9 $ $ \dfrac{9}{54} \cdot \dfrac{z^5}{z^3} = \dfrac{9 \cdot 1}{9 \cdot 6} \cdot \dfrac{z^5}{z^3} $ $\phantom{ \dfrac{9}{54} \cdot \dfrac{5}{3}} = \dfrac{1}{6} \cdot \dfrac{z^5}{z^3} $ $ \dfrac{z^5}{z^3} = \dfrac{z \cdot z \cdot z \cdot z \cdot z}{z \cdot z \cdot z} = z^2 $ $ \dfrac{1}{6} \cdot z^2 = \dfrac{z^2}{6} $